While most papers consider a fixed dimensional framework, high dimensional statistical problems received much less attention in the field of diffusion processes. The only notable exceptions are recent articles [1]}, [2]}, [3]}, [4]}, [5]} that investigate parametric inference for high dimensional Ornstein-Uhlenbeck models or related processes with linear drift. Their approach is based upon the Lasso method and Dantzig selection, which have been popularised in the context of classical discrete linear models; see e.g. [6]}, [7]} among many other references. Due to a more complex probabilistic structure of diffusion models, statistical analysis of Lasso and Dantzig estimators are far from trivial even in the Ornstein-Uhlenbeck setting. In particular, concentration inequalities for functionals of diffusion processes, which build a backbone for statistical applications, turn out to pose serious challenges.
